Metal surfaces, such as those encountered in industrial heat exchangers, are subject to accumulated corrosion product formation and deposit formation. Typically, in cooling water systems, accumulations of iron oxides are troublesome in that they reduce heat transfer efficiency of heat exchangers and the like. In many instances, these deposits must be mechanically cleaned when they are present in excessive amounts. The present invention is directed toward methods and compositions for chemically cleaning iron oxides, as well as other corrosion by-products and deposits, from metal surfaces, particularly from heat exchange surfaces in cooling water systems. The methods of the present invention provide significant improvement over the traditionally employed cleaning methods in that, in accordance with the present invention, cleaning treatment may be made when the system is still operating. Moreover the methods are performed without requiring pH depression of the system.